4.4 - Solving IVP With the Laplace Transform

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Last updated 9:30 PM on 6/28/26
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4 Terms

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IVP With Laplace Transforms

IVPs can only be solved with Laplace transforms if the initial condition for the desired function is given at t = 0. If any other point is given, we must shift the value over and perform a series of substitutions.

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Laplacian of an Nth Derivative

Solving differential equations with the Laplacian requires that we modify the differential equation such that it is transformed from the t-domain into the s-domain; from there, we isolated the Y(s) function and solve for the inverse Laplacian using the rules defined in 4.3.

<p>Solving differential equations with the Laplacian requires that we modify the differential equation such that it is transformed from the t-domain into the s-domain; from there, we isolated the Y(s) function and solve for the inverse Laplacian using the rules defined in 4.3. </p><p></p><p></p>
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Laplacian of the First and 2nd Order Derivatives

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